Bernoulli$(p)$ on $\{0,1\}$
1/2
nats:
0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875
Bernoulli$(p)$ on $\{0,1\}$
1/3
nats:
0.6365141682948128184504238226170746592638238015825792823209076606418985452388124898030402034827862971
Bernoulli$(p)$ on $\{0,1\}$
1/3
bits:
0.9182958340544895147870722772811498420931477410258143937890859878744315611276918958556138082514215754
Bernoulli$(p)$ on $\{0,1\}$
1/4
nats:
0.5623351446188083502880303152244588576653823503534484194403392687586665240254327060565148378825383085
Bernoulli$(p)$ on $\{0,1\}$
1/4
bits:
0.8112781244591328639096957920391376184301391942306392046581855090941763291542310781082896438114338184
Bernoulli$(p)$ on $\{0,1\}$
1/5
nats:
0.5004024235381878795331879388931051306048011392921093153195598762847491925561462196607525548989097107
Bernoulli$(p)$ on $\{0,1\}$
1/5
bits:
0.7219280948873623478703194294893901758648313930245806120547563958159347766086252158501397433593701551
Bernoulli$(p)$ on $\{0,1\}$
1/10
nats:
0.3250829733914482395065500282238179392356184845478239629108781004200828818838563398634888464248805385
Bernoulli$(p)$ on $\{0,1\}$
1/10
bits:
0.4689955935892812212535893303833204600971654591781147032344016176419579665787798033100348885068113193
Bernoulli$(p)$ on $\{0,1\}$
11/100
nats:
0.3465153369186661520863132845963983869516674787760962287376525101445031561505328626958518310638733583
Bernoulli$(p)$ on $\{0,1\}$
11/100
bits:
0.4999159581645279956404995941302756626364007555431767231334216282975329506755548763322804854150763222
Bernoulli$(p)$ on $\{0,1\}$
2/5
nats:
0.6730116670092564359967193424894015895069069658307659492235592874943249629886144982636190944063728825
Bernoulli$(p)$ on $\{0,1\}$
2/5
bits:
0.9709505944546686389980760631207002706089427484090919757813048030912758399320100783367714584085172098
Bernoulli$(p)$ on $\{0,1\}$
1/6
nats:
0.4505612088663046886451779140255459064516562302925732709281677669024054254319222119543675167325011007
Bernoulli$(p)$ on $\{0,1\}$
1/6
bits:
0.6500224216483542248951394193733246955391215801719972170767889913611525806205042159804973554519464462
Bernoulli$(p)$ on $\{0,1\}$
1/7
nats:
0.4101163182884090186946578648311492101602355648535714405833549986825330783049518256623907141791708616
Bernoulli$(p)$ on $\{0,1\}$
1/7
bits:
0.5916727785823273804816216509908452297040428479440141604295037344636652250384570757644777349547065776
Bernoulli$(p)$ on $\{0,1\}$
2/7
nats:
0.5982695885852572348427440421507095390972265810014184573444473676007681223981152314501733493794807514
Bernoulli$(p)$ on $\{0,1\}$
2/7
bits:
0.8631205685666310018203125818822663973090042023771546322096085842017960084274606894620468967706606743
Bernoulli$(p)$ on $\{0,1\}$
3/7
nats:
0.6829081047004716551734109316670383498447314798175339901494582818147753119787286070065508013860792746
Bernoulli$(p)$ on $\{0,1\}$
3/7
bits:
0.9852281360342514582475097698256237334582490226693631863391120149812787512360393168454550813481729671
Bernoulli$(p)$ on $\{0,1\}$
1/8
nats:
0.3767701612564367862845127138617474407940512646966372224600736472847984860010235375033887947248684765
Bernoulli$(p)$ on $\{0,1\}$
1/8
bits:
0.5435644431995964059882768474221480424391017022796268142823697414384692572455811368143716257260655630
Bernoulli$(p)$ on $\{0,1\}$
3/8
nats:
0.6615632381579820598530048172622152902801905974794111417661247211947586386348196813461503991258692726
Bernoulli$(p)$ on $\{0,1\}$
3/8
bits:
0.9544340029249649645358982525886999492995499764749567197948700071621289291967247791478074823061105623
Bernoulli$(p)$ on $\{0,1\}$
1/9
nats:
0.3488320958430318910112048166232472277603140906848182258142419752926055945180320254649293043036810108
Bernoulli$(p)$ on $\{0,1\}$
1/9
bits:
0.5032583347756456962408112212289663508529621487182954542448386424155297889220504583778942831695098175
Bernoulli$(p)$ on $\{0,1\}$
2/9
nats:
0.5297061990576545211713867575096501600049151850017723670852674374361167771923430108888608269488043927
Bernoulli$(p)$ on $\{0,1\}$
2/9
bits:
0.7642045065086202793415017522708757219099414396335192891625006348052802398070114688795579504815680958
Bernoulli$(p)$ on $\{0,1\}$
4/9
nats:
0.6869615765973233440858622918676791046025357993983177209662020524618725959599016506363897311344366715
Bernoulli$(p)$ on $\{0,1\}$
4/9
bits:
0.9910760598382221696461893159570829198169447081490840031033073114066771352505920051278166479698597313
Bernoulli$(p)$ on $\{0,1\}$
3/10
nats:
0.6108643020548934630256709631973806854608950105746453085913464959200184177853213027225515296339686028
Bernoulli$(p)$ on $\{0,1\}$
3/10
bits:
0.8812908992306926182248192242427636571881684325405377453439263926043807140667825565449529014647961329
Bernoulli$(p)$ on $\{0,1\}$
1/11
nats:
0.3046360973492381040455877100702527474570691370021690151882696173418712514792799128605117942848181566
Bernoulli$(p)$ on $\{0,1\}$
1/11
bits:
0.4394969869215133035899817471899837079170211683866947876266594677118444591667227019366369871420185296
Bernoulli$(p)$ on $\{0,1\}$
2/11
nats:
0.4741393130578373564302273500086005889302677348892352989034897069067841219246593644444355952171788848
Bernoulli$(p)$ on $\{0,1\}$
2/11
bits:
0.6840384356390416865477902293566386716417170403667990632942973019318062469656134322184868857845742744
Bernoulli$(p)$ on $\{0,1\}$
3/11
nats:
0.5859526183035508622256429756229643227531182268361104066639855974256709141924639789694576977885216307
Bernoulli$(p)$ on $\{0,1\}$
3/11
bits:
0.8453509366224364794392524256491157290414639599474550548248691035787583757761023811125057152183309682
Bernoulli$(p)$ on $\{0,1\}$
4/11
nats:
0.6554817739013927612369139256226137859977437464869562341111885159023728952748692040422805165402302288
Bernoulli$(p)$ on $\{0,1\}$
4/11
bits:
0.9456603046006400969181098448509915350225782182487693907908887304088537158986228158472161179967663528
Bernoulli$(p)$ on $\{0,1\}$
5/11
nats:
0.6890092384766585551638835037455700421884385880791792802462508440254624939434084477998234460638345449
Bernoulli$(p)$ on $\{0,1\}$
5/11
bits:
0.9940302114769564536471784275318066012593184882928781237665927451512157788282658568563657023500477407
Bernoulli$(p)$ on $\{0,1\}$
1/12
nats:
0.2868359830561606448395945333708436492952595437672942160257006192545890485708647444332089264708209051
Bernoulli$(p)$ on $\{0,1\}$
1/12
bits:
0.4138168503036336966043228177825062966151855091508603284190178126252951597176750725385801172384294608
Bernoulli$(p)$ on $\{0,1\}$
5/12
nats:
0.6791932659915257261679373239861124820411908366752918825778068103797853723411005899466525020914862353
Bernoulli$(p)$ on $\{0,1\}$
5/12
bits:
0.9798687566511528071666237466086692971088691287853236816211839839101049090378188137943033323357277195
Bernoulli$(p)$ on $\{0,1\}$
1/20
nats:
0.1985152433458725564266475158490799153010913247548558525429456858721381646860597715634100674610640849
Bernoulli$(p)$ on $\{0,1\}$
1/20
bits:
0.2863969571159561287664759777278974743059992018461232982023079014945978288134335733875670918958024613
Bernoulli$(p)$ on $\{0,1\}$
1/25
nats:
0.1679441477341729543404547292072020865321713860696608382924307953153898226527301401167102498154905962
Bernoulli$(p)$ on $\{0,1\}$
1/25
bits:
0.2422921890824147615450494727888765033202409546643794060719902432724152545346662116788902307973755978
Bernoulli$(p)$ on $\{0,1\}$
2/25
nats:
0.2787693717685874089059274914703407246381728081350141408568968349045326993517255176692696852458904974
Bernoulli$(p)$ on $\{0,1\}$
2/25
bits:
0.4021791902022728532300224743491250147907436706420105693746245581782736592995069112783853229256191531
Bernoulli$(p)$ on $\{0,1\}$
1/50
nats:
0.09803911327973198061225941076191957703801677291684276856557109856409506639095448000232042595054971624
Bernoulli$(p)$ on $\{0,1\}$
1/50
bits:
0.1414405425418206451543789972043919667932505991555252881020210124540406894473521781644719283451271714
Bernoulli$(p)$ on $\{0,1\}$
3/50
nats:
0.2269675225006044055233424441093570184855659375289151396334162864250928190964406985996657696652927617
Bernoulli$(p)$ on $\{0,1\}$
3/50
bits:
0.3274449191544761950128524133651065220106155539650904498938617310481118099811849762154853731295092786
Bernoulli$(p)$ on $\{0,1\}$
1/100
nats:
0.05600153435484734045207319807664951317668188737045903416557898929363863110775486011793105472539861738
Bernoulli$(p)$ on $\{0,1\}$
1/100
bits:
0.08079313589591117282486633370356863526903104839309833380744890637142774866160230872376776008689410701
Bernoulli$(p)$ on $\{0,1\}$
3/100
nats:
0.1347421681797667398409055792082097816681308049438455532176676342286484175333051798837716748515383206
Bernoulli$(p)$ on $\{0,1\}$
3/100
bits:
0.1943918578315761608655943296458712861413420598012773323289368456381923157762491710228600763858658681
Bernoulli$(p)$ on $\{0,1\}$
7/100
nats:
0.2536389469216914149669073251653647230869976220647081450274849537549122188330311265755013701587141808
Bernoulli$(p)$ on $\{0,1\}$
7/100
bits:
0.3659236509002232152780288416678172280775727639928899609816645906900039985197769117370448800692025383
Bernoulli$(p)$ on $\{0,1\}$
9/100
nats:
0.3025378230974980861302941983649403040231137431981688933150343707334457242057590494943613968669162964
Bernoulli$(p)$ on $\{0,1\}$
9/100
bits:
0.4364698170641029793456742550136151366876848374054825138011400363934816799136172495991028494327416565
Bernoulli$(p)$ on $\{0,1\}$
3/20
nats:
0.4227090878059908715138323654120043647295054786177327431911516832153933982334642620355375310320796672
Bernoulli$(p)$ on $\{0,1\}$
3/20
bits:
0.6098403047164004236363024787083739986412820418776108680787757929060780097491966734190559930545252865
Bernoulli$(p)$ on $\{0,1\}$
7/20
nats:
0.6474466390346324582135832789199707771801978035412421885208417760515612459229563355064565263439437837
Bernoulli$(p)$ on $\{0,1\}$
7/20
bits:
0.9340680553754910060077019431913978159819884127722570475677030005934666081953912254800936489670456977
Bernoulli$(p)$ on $\{0,1\}$
9/20
nats:
0.6881388137135884719454338950314465265919213512829742772225707701654058745980189334643262633522089707
Bernoulli$(p)$ on $\{0,1\}$
9/20
bits:
0.9927744539878082936523047042371691906942210869763752184225381015794645307476924155898671013252954684
Bernoulli$(p)$ on $\{0,1\}$
3/25
nats:
0.3669249912727096351724146225291630307439616918963537717985944705227674838521027959962259948095443095
Bernoulli$(p)$ on $\{0,1\}$
3/25
bits:
0.5293608652873643685107507045863445670196413145261075940995570248477668205283112538132534863560972911
Bernoulli$(p)$ on $\{0,1\}$
4/25
nats:
0.4396698794013429331275020840785662124679994241218808247436472137074097253696435031509211186901582043
Bernoulli$(p)$ on $\{0,1\}$
4/25
bits:
0.6343095546405660530682439195878766051129563177759188750377555135982775288257471305233606484845691274
Bernoulli$(p)$ on $\{0,1\}$
6/25
nats:
0.5510799280869727993996632522062380452972767038257764123311561609258824222013327060424324048519607145
Bernoulli$(p)$ on $\{0,1\}$
6/25
bits:
0.7950402793845222369086667510221102283802415752601999185181733590849364203104510627248740515675449770
Bernoulli$(p)$ on $\{0,1\}$
7/25
nats:
0.5929533174474744453824596296699608110460724842499713175918170936926004237917590267454950942125595312
Bernoulli$(p)$ on $\{0,1\}$
7/25
bits:
0.8554508105601306443635033708690119526960425837014690776235872863529982675119600654487945230690342218
Bernoulli$(p)$ on $\{0,1\}$
8/25
nats:
0.6268694575724263175912922896987997294987445309928839445073213120747411467797753312584144520042952772
Bernoulli$(p)$ on $\{0,1\}$
8/25
bits:
0.9043814577244938981278739716277053910020010340546831561834186278489159270650306252580861434650350044
Bernoulli$(p)$ on $\{0,1\}$
9/25
nats:
0.6534181947937017792888278649352247574317291629424023880273750384262744120554986011602542956096402776
Bernoulli$(p)$ on $\{0,1\}$
9/25
bits:
0.9426831892554922450939468193363524654225964125105748605813708803622788292053122666842375447777167759
Bernoulli$(p)$ on $\{0,1\}$
11/25
nats:
0.6859298002523728856816159678029588604106041689969866788842867016495604294493035448068714623379973932
Bernoulli$(p)$ on $\{0,1\}$
11/25
bits:
0.9895875212220556028454163007696061970612660042081444338725967020329044051776142840693011554971860555
Bernoulli$(p)$ on $\{0,1\}$
12/25
nats:
0.6923469670899614975434446465157477609691877805209629624988860281437012105707830048915245749701513448
Bernoulli$(p)$ on $\{0,1\}$
12/25
bits:
0.9988455359952018052365015856703471660381649414254308829307504840138577068267851656129490630118574079
Bernoulli$(p)$ on $\{0,1\}$
7/50
nats:
0.4049634850639385117173568423510782343966538617576924744968118436168315270689522102335297750282382286
Bernoulli$(p)$ on $\{0,1\}$
7/50
bits:
0.5842388116428558932584013437637860470271851978798096034768223991415758509735448809869345518282157860
Bernoulli$(p)$ on $\{0,1\}$
9/50
nats:
0.4713934868100941705457165367277683709849496571736735557536902459190711863736718619025293555248051721
Bernoulli$(p)$ on $\{0,1\}$
9/50
bits:
0.6800770457282798420211963669887812740073215231451163427962301828881947623011214152248698586045953259
Bernoulli$(p)$ on $\{0,1\}$
11/50
nats:
0.5269079614313803255151117115377048397927757030163527962379738178782774109005432338965305211839054245
Bernoulli$(p)$ on $\{0,1\}$
11/50
bits:
0.7601675029619655927333487420995871317521162190020278730252078088725931536254869812218589368202125547
Bernoulli$(p)$ on $\{0,1\}$
13/50
nats:
0.5730569171314204184124532565402981085912757627555860865797885755864383711077964098269657357708458331
Bernoulli$(p)$ on $\{0,1\}$
13/50
bits:
0.8267463724926178954626924774382898511628148440260723519532811945278800156184080783876198514948409372
Bernoulli$(p)$ on $\{0,1\}$
17/50
nats:
0.6410354778811556359321644000078365220770435268564274964757620133348472963056754605898963225912247661
Bernoulli$(p)$ on $\{0,1\}$
17/50
bits:
0.9248187049730300280832091014586606228402215940249177631792198715638897007816517644262134441165950950
Bernoulli$(p)$ on $\{0,1\}$
19/50
nats:
0.6640641265641080113392384825769060324975365867056547244123856976717318923101335111821547019044230378
Bernoulli$(p)$ on $\{0,1\}$
19/50
bits:
0.9580420222262995786393048467853395285057360701880222838708081862141869451469294095401414294441125981
Bernoulli$(p)$ on $\{0,1\}$
21/50
nats:
0.6802920001921534643222018573870468335403637321121626632898915053874075988173710329982429701597476654
Bernoulli$(p)$ on $\{0,1\}$
21/50
bits:
0.9814538950336535443869728609990973161847304618684965617035069557979776659221987888285936992598062114
Bernoulli$(p)$ on $\{0,1\}$
23/50
nats:
0.6899437584583995007873472014633699911142731943978361448163986983068339492178565013596090579941543107
Bernoulli$(p)$ on $\{0,1\}$
23/50
bits:
0.9953784388202257605302735774684899390693038878837665788037493745484924772315178002032380354548767795
Bernoulli$(p)$ on $\{0,1\}$
13/100
nats:
0.3863867062886037571857195176877765367539751240201396552611426093550554979124103060047746073524509582
Bernoulli$(p)$ on $\{0,1\}$
13/100
bits:
0.5574381850279890919980975402644629303820588840578026116678169285958991081249152048618969720906806419
Bernoulli$(p)$ on $\{0,1\}$
17/100
nats:
0.4558862130273583579089200789984594281378786280874831509701323122561349198606844398710436261272451452
Bernoulli$(p)$ on $\{0,1\}$
17/100
bits:
0.6577047787442194485589567395811571743419464154440596113101878435693252880977042105265260799558671595
Bernoulli$(p)$ on $\{0,1\}$
19/100
nats:
0.4862229646617922805136731296810529600692315102650032529240337160318980959342144229457892716577140488
Bernoulli$(p)$ on $\{0,1\}$
19/100
bits:
0.7014714598838974240097559902355563230360976668898311254623844920544439056044903606355762176914208671
Bernoulli$(p)$ on $\{0,1\}$
21/100
nats:
0.5139566706172255583742303557216156454853445996087161135502828775121328583125610314578339280033369481
Bernoulli$(p)$ on $\{0,1\}$
21/100
bits:
0.7414827399312737247749839139975431694082553731501794672780687509255333900911375574231531097923819016
Bernoulli$(p)$ on $\{0,1\}$
23/100
nats:
0.5392763414970503752916115905679853552771859855344013913749421136315785880459157466220729899093179242
Bernoulli$(p)$ on $\{0,1\}$
23/100
bits:
0.7780113035465376851091588425739962166398542304284837420834188385250489489295118204051446759584843401
Bernoulli$(p)$ on $\{0,1\}$
27/100
nats:
0.5832588401285969937685948015313465176772660486648526010066932259606681594255956732126452431106266120
Bernoulli$(p)$ on $\{0,1\}$
27/100
bits:
0.8414646362081756109623777816243647077866085660754053029951927936853304472727456362407091747826866803
Bernoulli$(p)$ on $\{0,1\}$
29/100
nats:
0.6021516825926799510089213018995198409094948982554482324131590805193192229795242239808851866484472893
Bernoulli$(p)$ on $\{0,1\}$
29/100
bits:
0.8687212463394045171331143727821865588303231806267737901669946696110155702224036881829152128025850146
Bernoulli$(p)$ on $\{0,1\}$
31/100
nats:
0.6191006644255870580785633013350196220307110066709646571460756987947645781591130655860046880579681780
Bernoulli$(p)$ on $\{0,1\}$
31/100
bits:
0.8931734583778567339246983834381235866810045884911082939950146810637409411247132006559308378358182381
Bernoulli$(p)$ on $\{0,1\}$
33/100
nats:
0.6341786357122056303561623628921080208475227862180210892897639602022529079973776653408606516097084516
Bernoulli$(p)$ on $\{0,1\}$
33/100
bits:
0.9149263727797275312524996061820517868268324291981865540868187383021143449858553576497711790813168115
Bernoulli$(p)$ on $\{0,1\}$
37/100
nats:
0.6589556806830627302454062841955073470319727875122837136029074550498208899790204293073757375448326983
Bernoulli$(p)$ on $\{0,1\}$
37/100
bits:
0.9506720926870659001330995740316032063367226192192568161804551205533600568760491737913827901693167806
Bernoulli$(p)$ on $\{0,1\}$
39/100
nats:
0.6687480868518093995926298116688441392630612979706236420948932383419129425675087674023383313389868799
Bernoulli$(p)$ on $\{0,1\}$
39/100
bits:
0.9647995485050872137708803796580273274241008341902441677914674972808395228839983947338955500568698005
Bernoulli$(p)$ on $\{0,1\}$
41/100
nats:
0.6768585467349506925871402059287697057705000790988641098706563574636259192117831713854338059331280804
Bernoulli$(p)$ on $\{0,1\}$
41/100
bits:
0.9765004687578240388462205330542698786354584526138131905652535742739104794894937303741043854596802572
Bernoulli$(p)$ on $\{0,1\}$
43/100
nats:
0.6833149135741659396422252074080980220373986208590065094788180330916471872781212262157985919842787321
Bernoulli$(p)$ on $\{0,1\}$
43/100
bits:
0.9858150371789198271295206844703603250549023286903266758793299063904170029958517992832138276339418887
Bernoulli$(p)$ on $\{0,1\}$
47/100
nats:
0.6913460990017392601335674508904061537302710322650953268469082598263982030169288313216004554873277338
Bernoulli$(p)$ on $\{0,1\}$
47/100
bits:
0.9974015885677395658015454546641314812574173062690661608682496564186477257289225805159122809713206354
Bernoulli$(p)$ on $\{0,1\}$
49/100
nats:
0.6929471672244781854938994948486296376376562213589899254701680985212256506577115516693766639089526317
Bernoulli$(p)$ on $\{0,1\}$
49/100
bits:
0.9997114417528099196965284011648935192482050306833193643287624253897798055430135832143676578834297580
binomial $\operatorname{Binom}(n,p)$
2, 1/2
nats:
1.039720770839917964125848182187264852113250201540382881181020014240090432954542073408794990494628031
binomial $\operatorname{Binom}(n,p)$
2, 1/3
nats:
0.9649629230074277216043000356971819549385364323383784516992908726200665918244273282256967060782753997
binomial $\operatorname{Binom}(n,p)$
2, 1/3
bits:
1.392147223664534585129700110117855239741851037607184343133727531304418677810939347266783172058398706
binomial $\operatorname{Binom}(n,p)$
2, 1/4
nats:
0.8647400965276372095445985849021015023024521503218011185854235339573104398122298937608309281414196092
binomial $\operatorname{Binom}(n,p)$
2, 1/4
bits:
1.247556248918265727819391584078275236860278388461278409316371018188352658308462156216579287622867637
binomial $\operatorname{Binom}(n,p)$
2, 1/10
nats:
0.5253994542821063233179982745851640962176469449108019800800337991313549118131676309179222939904057133
binomial $\operatorname{Binom}(n,p)$
2, 1/10
bits:
0.7579911871785624425071786607666409201943309183562294064688032352839159331575596066200697770136226387
binomial $\operatorname{Binom}(n,p)$
3, 1/2
nats:
1.255482325178753659705262436682635425740882484713703673561019278252060145995127421662378164878956996
binomial $\operatorname{Binom}(n,p)$
3, 1/2
bits:
1.811278124459132863909695792039137618430139194230639204658185509094176329154231078108289643811433818
binomial $\operatorname{Binom}(n,p)$
3, 1/3
nats:
1.177134312439031994421107976569540174693144366199238212472926759500699440237364824826710107239204165
binomial $\operatorname{Binom}(n,p)$
3, 1/3
bits:
1.698245835016031090058724202544905187106233617949122474396756193929229198186836645885321108142205898
binomial $\operatorname{Binom}(n,p)$
3, 1/4
nats:
1.069036021480613349454265499904455864131933612285048691720252243604909032140830574303135651564890626
binomial $\operatorname{Binom}(n,p)$
3, 1/4
bits:
1.542292966721748239661359220146766069113021978364897017468195659103161234328366542906086164292876819
binomial $\operatorname{Binom}(n,p)$
3, 1/10
nats:
0.6786236022339551018429338707023718774520330030313295367642668311781251864825445985345902854749339516
binomial $\operatorname{Binom}(n,p)$
3, 1/10
bits:
0.9790469055731314947682584762840509229263464874573742233801516361997773782318625980490889372925501326
binomial $\operatorname{Binom}(n,p)$
4, 1/2
nats:
1.407531740719315302947017354981766351955378893512138997666274649806097897713470265887785325310449522
binomial $\operatorname{Binom}(n,p)$
4, 1/2
bits:
2.030639062229566431954847896019568809215069597115319602329092754547088164577115539054144821905716909
binomial $\operatorname{Binom}(n,p)$
4, 1/3
nats:
1.330575170632721091420485089014089007531939806809174743231983914239041097966424457632203232163773415
binomial $\operatorname{Binom}(n,p)$
4, 1/3
bits:
1.919614200201813017729897323263517933678324966762275532552170325460857633806266280946717808338598427
binomial $\operatorname{Binom}(n,p)$
4, 1/4
nats:
1.221565833659991821839584204247365512438242176318701821881851540630437905895109220322547363651682035
binomial $\operatorname{Binom}(n,p)$
4, 1/4
bits:
1.762346970340662573613385109667557928904033425299924094942856710809442409191551803151115037567701035
binomial $\operatorname{Binom}(n,p)$
4, 1/10
nats:
0.8040182879587177743067798687690621806963613112249071209060917309992707804463660403917509940648632332
binomial $\operatorname{Binom}(n,p)$
4, 1/10
bits:
1.159953196822076694595705608857417958062934856498604233399456891557134492444313387101556722946226189
binomial $\operatorname{Binom}(n,p)$
5, 1/2
nats:
1.523670872042791627512178656479971573275061818199381372484867643276554295141485226434901544896975873
binomial $\operatorname{Binom}(n,p)$
5, 1/2
bits:
2.198192411043097798871575534853696710126720569039455676198665878922561146929413860140493990600590480
binomial $\operatorname{Binom}(n,p)$
5, 1/3
nats:
1.449403667489066084860237160194506660642426413181952575817963577494328849424632422492436763754927532
binomial $\operatorname{Binom}(n,p)$
5, 1/3
bits:
2.091047483332751717751134718945782391817118982762150452354899720765794418445820403852022349465059595
binomial $\operatorname{Binom}(n,p)$
5, 1/4
nats:
1.342052132566523583882733760066268972567977079209492375936745016871964149110500293925528073561723941
binomial $\operatorname{Binom}(n,p)$
5, 1/4
bits:
1.936171956268181281131634082264316669128656433497753760202343572095462577651304151905599586420148857
binomial $\operatorname{Binom}(n,p)$
5, 1/10
nats:
0.9102051201901215240709433923248535557782431572829811318473861097727732305734505727373294795585357283
binomial $\operatorname{Binom}(n,p)$
5, 1/10
bits:
1.313148413090031224815050845540697023469178840447007755535585344123164541872666990659542217628394518
binomial $\operatorname{Binom}(n,p)$
6, 1/2
nats:
1.617363315627128389966918714250924359837365210400365332805878227583171449896471574077313577437113687
binomial $\operatorname{Binom}(n,p)$
6, 1/2
bits:
2.333362034770989421647296763745659341231972269151355700908133886226205243784463743461831763835496657
binomial $\operatorname{Binom}(n,p)$
6, 1/3
nats:
1.545763808367196802452635494910837817042923694939978260573813180304124171241075868843431470972016842
binomial $\operatorname{Binom}(n,p)$
6, 1/3
bits:
2.230065780716992787662033985614445004118874234538538576705863965704691556000274400096243012328794548
binomial $\operatorname{Binom}(n,p)$
6, 1/4
nats:
1.440856527920919460432077525675939770006411968478258662503947525147001278635554779155403036938158925
binomial $\operatorname{Binom}(n,p)$
6, 1/4
bits:
2.078716567464000746382205519487883111425618649525581118175810664471000279725884770494286511045427382
binomial $\operatorname{Binom}(n,p)$
6, 1/10
nats:
1.002110637862436226051932947291347991489534602628447445848698273558356523695895103326601722383690184
binomial $\operatorname{Binom}(n,p)$
6, 1/10
bits:
1.445740047666212632827261301962397665583707336495933700840054299282351197378580422461225025509430387
binomial $\operatorname{Binom}(n,p)$
7, 1/2
nats:
1.695881445361670996358688139657080817963974579938456878433621993734205727526313416475057320297031337
binomial $\operatorname{Binom}(n,p)$
7, 1/2
bits:
2.446639751158890300705722424365029003381095644480167295888177215385140727448412960670499625959670500
binomial $\operatorname{Binom}(n,p)$
7, 1/3
nats:
1.626535701413680573567114364616051680458047647758885429942065524978065585811395039799714365243110877
binomial $\operatorname{Binom}(n,p)$
7, 1/3
bits:
2.346594990258368670950901543501773251061677141641386111512897412398032459891020490562429095001725405
binomial $\operatorname{Binom}(n,p)$
7, 1/4
nats:
1.524134585535896514630342112619284833959840272525586170043598391326785046542518668438653140103310558
binomial $\operatorname{Binom}(n,p)$
7, 1/4
bits:
2.198861408199993518043579140327136547480577967197673953445820564457696215241968592589016810428495319
binomial $\operatorname{Binom}(n,p)$
7, 1/10
nats:
1.082910859190992303564912194062541418212784813567036515428464073105962690306456366723661768263342398
binomial $\operatorname{Binom}(n,p)$
7, 1/10
bits:
1.562310126279651136284761267845191382640285092960968752337467915359471802172427997368855193733764657
binomial $\operatorname{Binom}(n,p)$
8, 1/2
nats:
1.763503329079247483278167569280108451044816166728980793826670179612784419080308747149677173743189448
binomial $\operatorname{Binom}(n,p)$
8, 1/2
bits:
2.544197507453808039366753681385027168878505724641944729066295398297453920344509000406247266259116884
binomial $\operatorname{Binom}(n,p)$
8, 1/3
nats:
1.695948272579713645438916984778606143121827492750268957935254309381349332340629337402011935267559686
binomial $\operatorname{Binom}(n,p)$
8, 1/3
bits:
2.446736162454956835993684719249583682080500428545900096086412823157010803575376940556707934050622086
binomial $\operatorname{Binom}(n,p)$
8, 1/4
nats:
1.595837294114369676694653248364852863263195544007878491596002442978044237500231091987077258496754252
binomial $\operatorname{Binom}(n,p)$
8, 1/4
bits:
2.302306550284463283861732180402866013381074617211053393782376774567872445793293006028539101717521166
binomial $\operatorname{Binom}(n,p)$
8, 1/10
nats:
1.154807284671601414243057134152881600841410779339380788319558607305643928509168452586671337438990939
binomial $\operatorname{Binom}(n,p)$
8, 1/10
bits:
1.666034742778168807811173194784590666177836565898479697157622116220670346281198911848700228831307049
binomial $\operatorname{Binom}(n,p)$
9, 1/2
nats:
1.822926834573997996266005095054228498151173787287080337775102112428642575344556221564822388534986430
binomial $\operatorname{Binom}(n,p)$
9, 1/2
bits:
2.629927504143322672413647083045100380678529183086380873725070730901268658978682520316241046324805250
binomial $\operatorname{Binom}(n,p)$
9, 1/3
nats:
1.756760907085107480677741667209285009718550286131301967604111963714379057904661180339680765544085236
binomial $\operatorname{Binom}(n,p)$
9, 1/3
bits:
2.534470248679281582119762935747840009911144538871508667020145815129613514165255459507535007280231807
binomial $\operatorname{Binom}(n,p)$
9, 1/4
nats:
1.658638696541375776155122971383506143823243886117256952747286024261726676008628495525784385418476966
binomial $\operatorname{Binom}(n,p)$
9, 1/4
bits:
2.392909822126777094291591711593222580537134956839141917193345974765601930175699187383030443367880770
binomial $\operatorname{Binom}(n,p)$
9, 1/10
nats:
1.219402874428558693918021801052092418844003646225019721269900663341728088948770709943679396920616172
binomial $\operatorname{Binom}(n,p)$
9, 1/10
bits:
1.759226479783828996260906124226044676266477424798807067541961685798568494318811989675353300808256882
binomial $\operatorname{Binom}(n,p)$
10, 1/2
nats:
1.875953605246800506692960297874478945330495958490238702822337421692753792599613674647690156903157003
binomial $\operatorname{Binom}(n,p)$
10, 1/2
bits:
2.706428963227331175844751481882337766996210323030402125814615204046131438887057606287973484258781968
binomial $\operatorname{Binom}(n,p)$
10, 1/3
nats:
1.810859198431020054279542127351776025378825695322652407590746420261968170471985282958591497206964644
binomial $\operatorname{Binom}(n,p)$
10, 1/3
bits:
2.612517585324595977735927761873749294940512965245128714879507784562360572609354003175446971683354461
binomial $\operatorname{Binom}(n,p)$
10, 1/4
nats:
1.714421065073478753632386779898649184044511456784000365870797830659595092711955503592799509206191304
binomial $\operatorname{Binom}(n,p)$
10, 1/4
bits:
2.473386768577082625068177223842009060145196262291783597879890570978942868770985238050624138376266954
binomial $\operatorname{Binom}(n,p)$
10, 1/10
nats:
1.277907356882020645932289901991356735574852853234219885785862127161218366575042463805581896636647146
binomial $\operatorname{Binom}(n,p)$
10, 1/10
bits:
1.843630606489213929328267185673058019830700398368619021117294450784011288278862618143965530651660796
binomial $\operatorname{Binom}(n,p)$
11, 1/2
nats:
1.923844833782542271472213089034851963857391544620839267063348853614451966369653662877243806019740297
binomial $\operatorname{Binom}(n,p)$
11, 1/2
bits:
2.775521401137925832314412034239436498091445501665986825685374835748906653045061574574979829949804086
binomial $\operatorname{Binom}(n,p)$
11, 1/3
nats:
1.859580604820305004750806980237817064301792910855838438628683118273423130092748622415911280676739561
binomial $\operatorname{Binom}(n,p)$
11, 1/3
bits:
2.682807716707553232362653582176159181465032329096729664617625434077764300886698081489518821176246733
binomial $\operatorname{Binom}(n,p)$
11, 1/4
nats:
1.764550932701843141139175916303753608398776163522874606429765081601829937030137982792276079136346058
binomial $\operatorname{Binom}(n,p)$
11, 1/4
bits:
2.545708880004944108174272669629846281496292419783576004978783940433562725591435995945144592067025673
binomial $\operatorname{Binom}(n,p)$
11, 1/10
nats:
1.331259000346267769842474684232134774601793098000503901799583421610676655525643797237299959021451493
binomial $\operatorname{Binom}(n,p)$
11, 1/10
bits:
1.920600757938359331089985155711253438116021159164284871301768515933466162195532703091429391981824952
binomial $\operatorname{Binom}(n,p)$
12, 1/2
nats:
1.967518195598394159277750416068395856704945619749199080800889913206479323649741324501279707718827392
binomial $\operatorname{Binom}(n,p)$
12, 1/2
bits:
2.838528743648604764756779742096431109094410660387833873506433244715359233431948193089327201629708826
binomial $\operatorname{Binom}(n,p)$
12, 1/3
nats:
1.903903781863056105409291068057162679085102764541849776768075627261607167059004648547929421338954977
binomial $\operatorname{Binom}(n,p)$
12, 1/3
bits:
2.746752544423573795726130518044522052930891027372741496709309054115823672556400004595765997712479090
binomial $\operatorname{Binom}(n,p)$
12, 1/4
nats:
1.810045979409239726339332418954955382546802233293567463171829125890985927248335542434358522003305778
binomial $\operatorname{Binom}(n,p)$
12, 1/4
bits:
2.611344358274716924694482053881504731778124439454574502591614414498090075074718813518813822298630057
binomial $\operatorname{Binom}(n,p)$
12, 1/10
nats:
1.380201408880747723023243158553807751568015980108189871924766439908903032129074241657233853598504047
binomial $\operatorname{Binom}(n,p)$
12, 1/10
bits:
1.991209728020215238778524813935511816710832896597269062425522309603763101462632575164785252877037141
binomial $\operatorname{Binom}(n,p)$
13, 1/2
nats:
2.007662963297866686739242088094012158482642197888944467558604312551021421341168047688690578401498435
binomial $\operatorname{Binom}(n,p)$
13, 1/2
bits:
2.896445400926273220223533311152290911410544464605119678836341712436857857689912763969120828908633311
binomial $\operatorname{Binom}(n,p)$
13, 1/3
nats:
1.944564116523508037302084514180325849070552122171924176917642001416635954401589378633568231470947976
binomial $\operatorname{Binom}(n,p)$
13, 1/3
bits:
2.805413007599093431670431630028159747835832159113235455035417998382400515029657444373386452851581045
binomial $\operatorname{Binom}(n,p)$
13, 1/4
nats:
1.851680671530137282023410308032413709292143787394824874559081524775212452266064072733033668156216679
binomial $\operatorname{Binom}(n,p)$
13, 1/4
bits:
2.671410522126474626400199531706340176230473786395871396952846644295148923934443322788040254013259026
binomial $\operatorname{Binom}(n,p)$
13, 1/10
nats:
1.425334317538911280471013833900516310823521037957303710637512457789162811219209125583111098650044819
binomial $\operatorname{Binom}(n,p)$
13, 1/10
bits:
2.056322751522242362882003948459146033711056622305512771762044044133964056409481845763110558009180826
binomial $\operatorname{Binom}(n,p)$
14, 1/2
nats:
2.044810607569574310097131987022595035381296932656343413460113955319074702427677818472436995414774400
binomial $\operatorname{Binom}(n,p)$
14, 1/2
bits:
2.950038123097773117199320809785227459133997815943419761231124115081723396005797455683095552738278515
binomial $\operatorname{Binom}(n,p)$
14, 1/3
nats:
1.982127051772631267038733603341220540414263206555848717639016629673747599504872062318668308121476102
binomial $\operatorname{Binom}(n,p)$
14, 1/3
bits:
2.859604868004236754469776584737670976291943473787932461472627890195730103528486426623993444107023148
binomial $\operatorname{Binom}(n,p)$
14, 1/4
nats:
1.890055593667081970476169651086092613558982076207029346128194209473706941914693162584327345882057333
binomial $\operatorname{Binom}(n,p)$
14, 1/4
bits:
2.726773831987944830725370862669671955253380132269404874652388584120976338497651020351738741439709388
binomial $\operatorname{Binom}(n,p)$
14, 1/10
nats:
1.467148496023943873448593335360874340216860559661202785474000903807950865698557665979142347740933686
binomial $\operatorname{Binom}(n,p)$
14, 1/10
bits:
2.116647859461444873591107353633652205046697234960516762738876580253625639947984603402871752715690359
binomial $\operatorname{Binom}(n,p)$
15, 1/2
nats:
2.079379967245641079165414630685158591940495514012834922444118236063811903470644124639919916748552804
binomial $\operatorname{Binom}(n,p)$
15, 1/2
bits:
2.999911166869141547410844698259566095586813102364131577409365213699961280416555189471445623651283084
binomial $\operatorname{Binom}(n,p)$
15, 1/3
nats:
2.017036179625133258761447271577200506491712295979448499982161637636627723088885626793584769199021101
binomial $\operatorname{Binom}(n,p)$
15, 1/3
bits:
2.909968093638800166761980069984400211981775606796396346171911535688404353602040669985071358389077182
binomial $\operatorname{Binom}(n,p)$
15, 1/4
nats:
1.925644313405758588822798446710057733093716389538935838120488855385162320497285236750530028335199396
binomial $\operatorname{Binom}(n,p)$
15, 1/4
bits:
2.778117501466520753740496601753406903430488237682881181251838058114618717334090389754011687505737723
binomial $\operatorname{Binom}(n,p)$
15, 1/10
nats:
1.506050493181588700357782924076941392319895512462625327165283464343927779588728314295235229483377822
binomial $\operatorname{Binom}(n,p)$
15, 1/10
bits:
2.172771577841455615401019754036382394778514585584508865771872561141571960643655921617190880454956768
binomial $\operatorname{Binom}(n,p)$
16, 1/2
nats:
2.111707237558766462059791986807525681437167382373984805166030901962917978572953483389504385970807223
binomial $\operatorname{Binom}(n,p)$
16, 1/2
bits:
3.046549559435364544578865033476697535494411851946415646661192579458723978332924687677702189318214814
binomial $\operatorname{Binom}(n,p)$
16, 1/3
nats:
2.049645691866555153783607320938430377950306813891715960870414527283978870942944137847467885732552658
binomial $\operatorname{Binom}(n,p)$
16, 1/3
bits:
2.957013675235307480372330645898418526045217670863791388735496255539816898038024052238917321607210808
binomial $\operatorname{Binom}(n,p)$
16, 1/4
nats:
1.958825853143070064467271159875180738062358981480849632420770970833024230602808771087457655761417193
binomial $\operatorname{Binom}(n,p)$
16, 1/4
bits:
2.825988344294600097214187337966283988204632578385470003423848941772561336401310126592304925408788228
binomial $\operatorname{Binom}(n,p)$
16, 1/10
nats:
1.542380641779777572018154504677993486041871252551152945643292856548860507977666793546346132900974247
binomial $\operatorname{Binom}(n,p)$
16, 1/10
bits:
2.225184903058821826216372768452124604793897925529678045674517416852147080759073635968683544745796152
binomial $\operatorname{Binom}(n,p)$
17, 1/2
nats:
2.142066530325249174617291687830349785979333504130304319077566546018774083162426432947215231842974671
binomial $\operatorname{Binom}(n,p)$
17, 1/2
bits:
3.090348760554465332574045553269944757295930225174113679038468876216670431307678348594015054430831425
binomial $\operatorname{Binom}(n,p)$
17, 1/3
nats:
2.080242829310522743310078917509452382916249236925365975101355818313948243667067264819786858514580974
binomial $\operatorname{Binom}(n,p)$
17, 1/3
bits:
3.001156013691117535260576531889433771540503604359976356509239810317407767375037218211634610726581333
binomial $\operatorname{Binom}(n,p)$
17, 1/4
nats:
1.989907672948883093653652768154109917629722539942970137279268115757963820559705245898996885621687110
binomial $\operatorname{Binom}(n,p)$
17, 1/4
bits:
2.870829931590250918030278062686599832125608554054968030938623758095748023318583079207722680814809374
binomial $\operatorname{Binom}(n,p)$
17, 1/10
nats:
1.576426450807346730890788572653416305536107825366155743086850928125608773686559391565242934226330080
binomial $\operatorname{Binom}(n,p)$
17, 1/10
bits:
2.274302622905948553378367093408530177574902440448449729105824597199499050886465271627594864875096358
binomial $\operatorname{Binom}(n,p)$
18, 1/2
nats:
2.170684369312037704678140431411315853507631963667937922350778279943722500086535067098495013706811253
binomial $\operatorname{Binom}(n,p)$
18, 1/2
bits:
3.131635574941663982078696160064133731513542973061895305641966178722482021647263575014206958952368244
binomial $\operatorname{Binom}(n,p)$
18, 1/3
nats:
2.109063762463817866757111455345178887374148964888516075259837294783182657564393302814035503089053049
binomial $\operatorname{Binom}(n,p)$
18, 1/3
bits:
3.042735831025168724453043928330984967764576287909762552910896012913782108827475846136043092430864647
binomial $\operatorname{Binom}(n,p)$
18, 1/4
nats:
2.019142243351521550461212400326495862325269580715468661394410802708049335124355849596686289743062591
binomial $\operatorname{Binom}(n,p)$
18, 1/4
bits:
2.913006501332656685897631666305193017424823527883154655377762153227574949442784919412622300203077247
binomial $\operatorname{Binom}(n,p)$
18, 1/10
nats:
1.608432756398207206950308126746680429323826431077520480175046630812473955497146535473313148754088853
binomial $\operatorname{Binom}(n,p)$
18, 1/10
bits:
2.320477961259059665996529035071245997653186804333746264626245860536318299127471355286244978220466233
binomial $\operatorname{Binom}(n,p)$
19, 1/2
nats:
2.197750160447903330211463800855270884725604101935983115893258022648254228604079301187936897321322294
binomial $\operatorname{Binom}(n,p)$
19, 1/2
bits:
3.170683257591113784053150292485944822693711318183845395158648384103295701683247472395632315510292690
binomial $\operatorname{Binom}(n,p)$
19, 1/3
nats:
2.136305054405391190264825348982171562692434447661947190835990225404521077153541291542956451294852026
binomial $\operatorname{Binom}(n,p)$
19, 1/3
bits:
3.082036707816685039779205644338042588001030369018941970369660121722540093694882436748177375745805662
binomial $\operatorname{Binom}(n,p)$
19, 1/4
nats:
2.046739195871583596483598754098660604185312464248675627170260455708059742177640008714625708201527896
binomial $\operatorname{Binom}(n,p)$
19, 1/4
bits:
2.952820487876998381131364604471839447130337948852399981874491013271162165829309370093380097919533524
binomial $\operatorname{Binom}(n,p)$
19, 1/10
nats:
1.638609542355849424047184301281468910599923447148408901065595702160905837717155888344549480768251747
binomial $\operatorname{Binom}(n,p)$
19, 1/10
bits:
2.364013860710117801164872244623699093337769290443405979520320787991693633508569158208675624181039703
binomial $\operatorname{Binom}(n,p)$
20, 1/2
nats:
2.223423915810262567239544677696427764524255001784966920674530494917648585734516288333786296496313194
binomial $\operatorname{Binom}(n,p)$
20, 1/2
bits:
3.207722657133385887058394919338853818057502457586999632608268480481497539630388631016398679455331662
binomial $\operatorname{Binom}(n,p)$
20, 1/3
nats:
2.162132088127826855342146759871157421967391186762613855327834613668725454243338782300492123243183177
binomial $\operatorname{Binom}(n,p)$
20, 1/3
bits:
3.119297241288914998405254548352603805258171437816086398419924694298172711294737962627160490456808272
binomial $\operatorname{Binom}(n,p)$
20, 1/4
nats:
2.072874365788884422878766277871792819603537415907228624388941131910824278702235934922448518078076433
binomial $\operatorname{Binom}(n,p)$
20, 1/4
bits:
2.990525567909478703261188214559997777502009048769751975121912005773330791313942086996857677547404871
binomial $\operatorname{Binom}(n,p)$
20, 1/10
nats:
1.667138051650713579803409935157578572182980761903829093350385429489717633412968525026779786858013876
binomial $\operatorname{Binom}(n,p)$
20, 1/10
bits:
2.405171799593773016977828137848264973610022741627892474692174321367237803634479624417841165835336386
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/2
nats:
1.386294361119890618834464242916353136151000268720510508241360018986787243939389431211726653992837375
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/3
nats:
1.909542504884438455351271467851223977791471404747737846962722981925695635716437469409120610448358891
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/3
bits:
2.754887502163468544361216831843449526279443223077443181367257963623294683383075687566841424754264726
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/4
nats:
2.249340578475233401152121260897835430661529401413793677761357075034666096101730824226059351530153234
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/4
bits:
3.245112497836531455638783168156550473720556776922556818632742036376705316616924312433158575245735274
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/5
nats:
2.502012117690939397665939694465525653024005696460546576597799381423745962780731098303762774494548554
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/5
bits:
3.609640474436811739351597147446950879324156965122903060273781979079673883043126079250698716796850775
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/10
nats:
3.250829733914482395065500282238179392356184845478239629108781004200828818838563398634888464248805385
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/10
bits:
4.689955935892812212535893303833204600971654591781147032344016176419579665787798033100348885068113193
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/100
nats:
3.150139426533328655330120769058167154106067988873602079433204637677301419550298751780471191489757803
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/100
bits:
4.544690528768436324004541764820687842149097777665242937576560257250299551595953421202549867409784747
geometric with success probability $p$ on $\{1,2,\ldots\}$
2/5
nats:
1.682529167523141089991798356223503973767267414576914873058898218735812407471536245659047736015932206
geometric with success probability $p$ on $\{1,2,\ldots\}$
2/5
bits:
2.427376486136671597495190157801750676522356871022729939453262007728189599830025195841928646021293025
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/10
nats:
2.036214340182978210085569877324602284869650035248817695304488319733394725951071009075171765446562009
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/10
bits:
2.937636330768975394082730747475878857293894775135125817813087975347935713555941855149843004882653776
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/20
nats:
3.970304866917451128532950316981598306021826495097117050858913717442763293721195431268201349221281698
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/20
bits:
5.727939142319122575329519554557949486119984036922465964046158029891956576268671467751341837916049225
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/20
nats:
2.818060585373272476758882436080029098196703190784884954607677888102622654889761746903583540213864448
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/20
bits:
4.065602031442669490908683191389159990941880279184072453858505286040520064994644489460373287030168577
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/20
nats:
1.849847540098949880610237939771345077657708010117834824345262217290174988351303815732732932411267954
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/20
bits:
2.668765872501402874307719837689708045662824036492162993050580001695618880558260644228838997048701993
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/20
nats:
1.529197363807974382100964211180992281315380780628831727161268378145346387995597629920725029671575490
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/20
bits:
2.206165453306240652560677120527042645987157971058611596494529114621032290550427590199704669611767708
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/25
nats:
4.198603693354323858511368230180052163304284651741520957310769882884745566318253502917756245387264906
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/25
bits:
6.057304727060369038626236819721912583006023866609485151799756081810381363366655291972255769934389945
geometric with success probability $p$ on $\{1,2,\ldots\}$
2/25
nats:
3.484617147107342611324093643379259057977160101687676760711210436306658741896568970865871065573631217
geometric with success probability $p$ on $\{1,2,\ldots\}$
2/25
bits:
5.027239877528410665375280929364062684884295883025132117182806977228420741243836390979816536570239413
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/25
nats:
3.057708260605913626436788521076358589533014099136281431654953921023062365434189966635216623412869246
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/25
bits:
4.411340544061369737589589204886204725163677621050896617496308540398056837735927115110445719634144092
geometric with success probability $p$ on $\{1,2,\ldots\}$
4/25
nats:
2.747936746258393332046888025491038827924996400761755154647795085671310783560271894693256991813488777
geometric with success probability $p$ on $\{1,2,\ldots\}$
4/25
bits:
3.964434716503537831676524497424228781955976986099492968985971959989234555160919565771004053028557046
geometric with success probability $p$ on $\{1,2,\ldots\}$
6/25
nats:
2.296166367029053330831930217525991855405319599274068384713150670524510092505552941843468353549836310
geometric with success probability $p$ on $\{1,2,\ldots\}$
6/25
bits:
3.312667830768842653786111462592125951584339896917499660492388996187235084626879428020308548198104071
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/25
nats:
2.117690419455265876365927248821288610878830300892754705685061048902144370684853666948196765044855468
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/25
bits:
3.055181466286180872726797753103614116771580656076675277227097451260708098257000233745694725246550792
geometric with success probability $p$ on $\{1,2,\ldots\}$
8/25
nats:
1.958967054913832242472788405308749154683576659352762326585379100233566083686797910182545162513422741
geometric with success probability $p$ on $\{1,2,\ldots\}$
8/25
bits:
2.826192055389043431649606161336579346881253231420884863073183212027862272078220703931519198328234389
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/25
nats:
1.815050541093616053580077402597846548421469897062228855631597328961873366820829447667373043360111882
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/25
bits:
2.618564414598589569705407831489867959507212256973819057170474667672996747792534074122882068826991044
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/25
nats:
1.558931364209938376549127199552179228205918565902242452009742503749000976021144420015616959859084985
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/25
bits:
2.249062548231944551921400683567286811502877282291237349710447050074782739040032463793866262493604672
geometric with success probability $p$ on $\{1,2,\ldots\}$
12/25
nats:
1.442389514770753119882176346907807835352474542752006171872679225299377522022464593524009531187815302
geometric with success probability $p$ on $\{1,2,\ldots\}$
12/25
bits:
2.080928199990003760909378303479889929246176961302981006105730175028870222555802428360310547941369600
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/50
nats:
4.901955663986599030612970538095978851900838645842138428278554928204753319547724000116021297527485812
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/50
bits:
7.072027127091032257718949860219598339662529957776264405101050622702034472367608908223596417256358569
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/50
nats:
3.782792041676740092055707401822616974759432292148585660556938107084880318274011643327762827754879362
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/50
bits:
5.457415319241269916880873556085108700176925899418174164897695517468530166353082936924756218825154643
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/50
nats:
2.892596321885275083695406016793415959976099012554946246405798882977368050492515787382355535915987347
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/50
bits:
4.173134368877542094702866741169900335908465699141497167691588565296970364096749149906675370201541328
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/50
nats:
2.618852704500523169698425204043157616583053650964853087520501366217062146520399232791829752915584290
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/50
bits:
3.778205809601554677895535372159895966707341795250646348867945460489970901672896751249276992247751811
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/50
nats:
2.395036188324456025068689597898658362694435013710694528354426444901260958638832881347866005381388293
geometric with success probability $p$ on $\{1,2,\ldots\}$
11/50
bits:
3.455306831645298148787948827725396053418710086372853968296399131239059789206759005553904258273693431
geometric with success probability $p$ on $\{1,2,\ldots\}$
13/50
nats:
2.204065065890078532355589448231915802274137549059946486845340675332455273491524653180637445272483973
geometric with success probability $p$ on $\{1,2,\ldots\}$
13/50
bits:
3.179793740356222674856509528608807119856980169331047507512619978953384675455415686106230198057080528
geometric with success probability $p$ on $\{1,2,\ldots\}$
17/50
nats:
1.885398464356340105682836470611283888461892726048316166105182392161315577369633707617342125268308135
geometric with success probability $p$ on $\{1,2,\ldots\}$
17/50
bits:
2.720055014626558906127085592525472420118298805955640479938881975187910884651916954194745423872338515
geometric with success probability $p$ on $\{1,2,\ldots\}$
19/50
nats:
1.747537175168705292997996006781331664467201543962249274769436046504557611342456608374091320801113257
geometric with success probability $p$ on $\{1,2,\ldots\}$
19/50
bits:
2.521163216384998891156065386277209285541410711021111273344232068984702487228761604053003761695033153
geometric with success probability $p$ on $\{1,2,\ldots\}$
21/50
nats:
1.619742857600365391243337755683444841762770790743244436404503584255732378136597697614864214666065870
geometric with success probability $p$ on $\{1,2,\ldots\}$
21/50
bits:
2.336794988175365581873744907140707895677929671115468004055968942376137299814759021020461188713824313
geometric with success probability $p$ on $\{1,2,\ldots\}$
23/50
nats:
1.499877735779129349537711307529065198074506944343122053948692822406160759169253263825237082595987632
geometric with success probability $p$ on $\{1,2,\ldots\}$
23/50
bits:
2.163866171348316870717986037974978128411530191051666475660324727279331472242430000441821816206253868
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/100
nats:
5.600153435484734045207319807664951317668188737045903416557898929363863110775486011793105472539861738
geometric with success probability $p$ on $\{1,2,\ldots\}$
1/100
bits:
8.079313589591117282486633370356863526903104839309833380744890637142774866160230872376776008689410701
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/100
nats:
4.491405605992224661363519306940326055604360164794851773922254474288280584443505996125722495051277353
geometric with success probability $p$ on $\{1,2,\ldots\}$
3/100
bits:
6.479728594385872028853144321529042871378068660042577744297894854606410525874972367428669212862195603
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/100
nats:
3.623413527452734499527247502362353186957108886638687786106927910784460269043301808221448145124488297
geometric with success probability $p$ on $\{1,2,\ldots\}$
7/100
bits:
5.227480727146045932543269166683103258251039485612713728309494152714342835996813024814926858131464833
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/100
nats:
3.361531367749978734781046648499336711367930479979654370167048563704952491175100549937348854076847737
geometric with success probability $p$ on $\{1,2,\ldots\}$
9/100
bits:
4.849664634045588659396380611262390407640942637838694597790444848816463110151302773323364993697129517
geometric with success probability $p$ on $\{1,2,\ldots\}$
13/100
nats:
2.972205432989259670659380905290588744261347107847228117393404687346580753172386969267496979634238140
geometric with success probability $p$ on $\{1,2,\ldots\}$
13/100
bits:
4.287986038676839169216134925111253310631222185060020089752437912276146985576270806629976708389851092
geometric with success probability $p$ on $\{1,2,\ldots\}$
17/100
nats:
2.681683606043284458287765170579173106693403694632253829236072425036087763886379058064962506630853795
geometric with success probability $p$ on $\{1,2,\ldots\}$
17/100
bits:
3.868851639671879109170333762242101025540861267317997713589340256290148753515907120744271058563924468
geometric with success probability $p$ on $\{1,2,\ldots\}$
19/100
nats:
2.559068235062064634282490156216068210890692159289490804863335347536305768074812752346259324514284467
geometric with success probability $p$ on $\{1,2,\ldots\}$
19/100
bits:
3.691955052020512757946084159134506963347882457314900660328339431865494240023633477029348514165372985
geometric with success probability $p$ on $\{1,2,\ldots\}$
21/100
nats:
2.447412717224883611305858836769598311834974283851029112144204178629204087202671578370637752396842610
geometric with success probability $p$ on $\{1,2,\ldots\}$
21/100
bits:
3.530870190148922498928494828559729378134549395953235558466994052026349476624464559157871951392294769
geometric with success probability $p$ on $\{1,2,\ldots\}$
23/100
nats:
2.344679745639349457789615611165153718596460806671310397282357015789472121938764115748143434388338801
geometric with success probability $p$ on $\{1,2,\ldots\}$
23/100
bits:
3.382657841506685587431125402495635724521105349689059748188777558804560647519616610457150765036888435
geometric with success probability $p$ on $\{1,2,\ldots\}$
27/100
nats:
2.160217926402211088031832598264246361767652032092046670395160096150622812687391382269056455965283748
geometric with success probability $p$ on $\{1,2,\ldots\}$
27/100
bits:
3.116535689659909670231028820830980399209661355834834455537751087723446101010169023113737684380321038
geometric with success probability $p$ on $\{1,2,\ldots\}$
29/100
nats:
2.076385112388551555203176903101792554860327235363614594528134760411445596481118013727190298787749273
geometric with success probability $p$ on $\{1,2,\ldots\}$
29/100
bits:
2.995590504618636265976256457869608823552838553885426862644809205555226104215185131665224871733051774
geometric with success probability $p$ on $\{1,2,\ldots\}$
31/100
nats:
1.997098917501893735737300972048450393647454860228918248858308705789563155351977630922595767928929607
geometric with success probability $p$ on $\{1,2,\ldots\}$
31/100
bits:
2.881204704444699141692575430445559957035498672551962238693595745366906261692623227922357541405865284
geometric with success probability $p$ on $\{1,2,\ldots\}$
33/100
nats:
1.921753441552138273806552614824569760144008443084912391787163515764402751507205046487456520029419550
geometric with success probability $p$ on $\{1,2,\ldots\}$
33/100
bits:
2.772504159938568276522726079339550869172219482418747133596420419097316196926834417120518724488838823
geometric with success probability $p$ on $\{1,2,\ldots\}$
37/100
nats:
1.780961299143412784447044011339209046032358885168334361088939067702218621564920079209123614986034320
geometric with success probability $p$ on $\{1,2,\ldots\}$
37/100
bits:
2.569384034289367297657025875761089746856007078970964368055284109603675829394727496733467000457612921
geometric with success probability $p$ on $\{1,2,\ldots\}$
39/100
nats:
1.714738684235408716904179004279087536571952046078522159217674970107469083506432736929072644458940718
geometric with success probability $p$ on $\{1,2,\ldots\}$
39/100
bits:
2.473844996166890291720206101687249557497694446641651712285814095591896212523072807009988589889409745
geometric with success probability $p$ on $\{1,2,\ldots\}$
41/100
nats:
1.650874504231587055090585868118950501879268485606985633830869164545429071248251637525448307153970928
geometric with success probability $p$ on $\{1,2,\ldots\}$
41/100
bits:
2.381708460384936680112733007449438728379166957594666318451837986033927998754862757010010696243122579
geometric with success probability $p$ on $\{1,2,\ldots\}$
43/100
nats:
1.589104450172478929400523738158367493110229350834898859253065193236388807623537735385578120893671470
geometric with success probability $p$ on $\{1,2,\ldots\}$
43/100
bits:
2.292593109718418202626792289465954244313726345791457385765883503233527913943841393681892622404516020
geometric with success probability $p$ on $\{1,2,\ldots\}$
47/100
nats:
1.470949146812211191773547767851927986660151132478926227333847361332762134078571981535320118058144115
geometric with success probability $p$ on $\{1,2,\ldots\}$
47/100
bits:
2.122131039505828863407543520561981875015781502700140767804786503018399416444516128757260172279405607
geometric with success probability $p$ on $\{1,2,\ldots\}$
49/100
nats:
1.414177892294853439783468356833938035995216778283652909122792037798419695219819493202809518181535983
geometric with success probability $p$ on $\{1,2,\ldots\}$
49/100
bits:
2.040227432148591672850057961561007182139193940170039519038290664060775113353088945335444199762101547
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/2
nats:
1.879446901369988737925788796157318555100512433922042600578113052861162305480701611006017410718057259
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/2
bits:
2.711468724220611478455312866757461691832922457629908654148941494435117824326743107673891892166375716
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/3
nats:
2.449867104579724689101935770018060700850781293299710434708526875716573623656414507411149302607820754
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/3
bits:
3.534411122614172302399089788662596008978492107551128562669327673613488531954707255572644391095372123
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/4
nats:
2.805417974802155386714640721728335314455627537410893676914064465364988721563584019301420108927106471
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/4
bits:
4.047362599867828479671397437794379190413741192229037728235451854040454717915132847439611885682872696
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/10
nats:
3.824231985038146674850500425972198754184672624619114773187337091564020102471937812117569704276518706
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
2, 1/10
bits:
5.517200520023490714553629076400888082127447847765227725887394437281408174615990746919639767794903455
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/2
nats:
2.159602485630811620012601119650848258667065315834938900741333872083865742214323643137821920133446330
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/2
bits:
3.115647796311050779535873450451879809622313225025739365623644668625130642093557685747070761375193152
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/3
nats:
2.730098044633693543146062168051642813179599074191337631500254290553572546766619188911606339561276595
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/3
bits:
3.938698910133685551761085832307448105028119671101382761408863728879034105161536477177912234858875932
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/4
nats:
3.083097240951922637197144180195810670198606399721134551957041829215929410504898952918999292105844901
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/4
bits:
4.447969100099784295686643272643995038981149913619978091953091028354179149934313319379988740428386180
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/10
nats:
4.096539445838805839523459194428109521218538623476097589951459824280402106997762802472410186292422924
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
3, 1/10
bits:
5.910057143317667488360733008613298969559669408420038695701362807682073655530623029481239210390949538
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/2
nats:
2.346363347587143987539751892729112036624632263462642478634989332204783342265270592599639057599919211
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/2
bits:
3.385086765687599754964928686428639950660618372377804012243372175484322094394964718989275094401232184
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/3
nats:
2.911513097736697861019405938318775954212687596456503724817299722978323273439689272213272012966385246
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/3
bits:
4.200425507587997834008370633356179386578991947856242305961671347912645883429980684748564575466487796
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/4
nats:
3.262086579310003689959415571992778032064618586465496322993423890925318072542832233048726092693040789
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/4
bits:
4.706196130920984546532648707880344135611277419271709713910260375029858122531974200756423899248507727
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/10
nats:
4.272837953295725805724313083039532558496559058474614057493275072199571602767671617094046043666500600
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
4, 1/10
bits:
6.164402125741891859177045220415489012993207890237866142348135519904411128973273457465634981136538946
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/2
nats:
2.483619150583802605562173905513994399670192904332732875099860366839411599285545380546957675711634023
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/2
bits:
3.583105032004111666070963738862561101686470002006546674905011373428116160649116775476381357539647803
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/3
nats:
3.044375976937700299109851396698909384452670977918133547065177045252981774097929905960529939050059743
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/3
bits:
4.392106124529513452275536562145327021989956085007890092699036251185265745372166310442733511973920097
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/4
nats:
3.393592382478125184568360171607053703134349869249672294010630521083591017269045755383931060565907164
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/4
bits:
4.895918900999753559794296683271328828771970765001241167663230603895475643094670293068877903314421277
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/10
nats:
4.403176828671754228578305727576861159781646038679826337222800037026905826897151266270601933316501943
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
5, 1/10
bits:
6.352441374881932690493257863936960449965086412926850424968971571687067591769433371396454255963040627
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/2
nats:
2.591291695951424195371350623153102952307365231053966774394307045355189284354839470362210447109646226
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/2
bits:
3.738443679245871263094694498391608695068929465023119394473423814144673706304638435421628761800973870
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/3
nats:
3.149085770859069736133955193010718286920116800760524741613002236811312536129417582341442892053557691
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/3
bits:
4.543170424952378464266099573547086029922628767699342378594929576539360368535108293680700451404071433
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/4
nats:
3.497565413071357586776615912664227567575294152321964867542326420592651734354784048226522660755759414
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/4
bits:
5.045920276622806423577129855224952410902265918418637868810974302361872666294011334140358178947896431
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/10
nats:
4.506575884046698504020046617684940330183166132751328752398296056598671644031170993073252399665853757
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
6, 1/10
bits:
6.501614679303968113533359252614631543666064412182277714875481114022307740191274032718326488264251596
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/2
nats:
2.679668528945075960943083140404993073002061525033255817421514110721922765458717757689812249592629283
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/2
bits:
3.865944497935284787361991451555035252110944017933382779306912505447064676374867209754016500579699738
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/3
nats:
3.235529793580250893536859058587691996264906378865365704046175513946143211890424686054166035138065781
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/3
bits:
4.667882787846719395976848212063342874633686453681245648202490340953250000767180855513199705020552695
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/4
nats:
3.583582543152124785753146295468219978536449249496344751414840284065868450574188126309736324810495951
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/4
bits:
5.170016763621830141983183997386615311088067034292921461156027373144744235381743384988088704263124433
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/10
nats:
4.592264428308361232133418250572350637019450815640842544996433250574679842373959487904250538182735884
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
7, 1/10
bits:
6.625237117171263373813948485285472273259823247244383130908027048066716246718626416397629415874875444
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/2
nats:
2.754588631980323463205976651105495546790927827281703094629101148286790838358658492693927024191928246
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/2
bits:
3.974031359047126534123026950376289469643360963045388132684340527005615789046151076936042622800236399
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/3
nats:
3.309168431412236876319500797284692877809412583333243660739313286505193885565360347218120097800379833
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/3
bits:
4.774120885464743981087356562640274070678265685955748297779692707724663715415949627289268445077347594
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/4
nats:
3.656951445667729262850747948648301419117847583415276396174313381087052256049068916813730275744625302
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/4
bits:
5.275865715436558513268217403783844332338630503472058785754601672851856275495216449273385438475914913
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/10
nats:
4.665421277814408941696014684628752712365488801277787455346415162704871219521067007584441335878993395
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
8, 1/10
bits:
6.730780141160698616611880324939210485640152621350730243767971172110116541585501401427538937871602923
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/2
nats:
2.819624074503889115839126687935684535990942074836195198494923473083851328800023206420327677550394053
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/2
bits:
4.067857669457893912876144909344075283008976027618465587599758205854999141655900020044966231105736001
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/3
nats:
3.373323834047520856084623522341011748335782853633496765441233330993080000289264146428976721398405721
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/3
bits:
4.866677566692902913013169420962884119884071767179663599843283630143199448511560274488109355225273307
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/4
nats:
3.720922351794979839946667254461993478464442545271333759307270753068916484315722201006571445163548637
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/4
bits:
5.368156224467516324364420347060658273452577784510998206696202208414721618492330165888221263506010427
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/10
nats:
4.729243471379188572086396087517198087965729499739399490243101528435308618002083080562252804923578886
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
9, 1/10
bits:
6.822856103315261702725647996690290815935359435862464307846333694509709045795941519733308448374570932
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/2
nats:
2.877098210794647635265328380692670580739269121320515312631039129165275179695762828767124516344119412
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/2
bits:
4.150775320863947630722171133737885449295870885246950094832225370424433250907809552109454928613195122
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/3
nats:
3.430168279359647660797625165510119006740096483615321154332986778280490677674774846616001543424642280
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/3
bits:
4.948686766046792137817818656654195383840529638592860536611923069072070882970474994817410560505475502
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/4
nats:
3.777632439167529815198128832458566399337494675942545817055974920014516285611858052542849012667986687
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/4
bits:
5.449971586288273998314207782771346610777598428328893835458247101761065774695882232563150202289125783
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/10
nats:
4.785843152910122319598680897013319929343095933543888146045893710117799204336282555136944715950496492
negative binomial $\operatorname{NB}(r,p)$, failures before the $r$th success with success probability $p$
10, 1/10
bits:
6.904512183175834472579459092817319189411425758731400099897986900147206831659834870993656702635258307
Poisson$(\lambda)$
1/2
nats:
0.9276374674957973741380689368997581161181488664823499650950432870081292570454866484877211846538914968
Poisson$(\lambda)$
1/2
bits:
1.338297974098983856413811741912613418168564396089567771516892892268879012163659973754392647533261072
Poisson$(\lambda)$
1
nats:
1.304842242256251484308800012107587605872065984275157220597445437553228920185141353023669020482477252
Poisson$(\lambda)$
1
bits:
1.882489432045529431148225220161389460789969828965417543855549868681617086658698595848528595674821755
Poisson$(\lambda)$
3/2
nats:
1.539404652817375537420505972498112187463117204944891761208332163402378303606451029641360422929993834
Poisson$(\lambda)$
3/2
bits:
2.220891458541024119128154395955314249913987338184135433427170610929808291199388515682229815447931185
Poisson$(\lambda)$
2
nats:
1.704882643932983838377586644492340397420976065766115801126708886596714230612459356368362295216890990
Poisson$(\lambda)$
2
bits:
2.459625735699780160326968433582661250941312804283989504850529101691252519175780838299821850064095362
Poisson$(\lambda)$
5/2
nats:
1.830726607926971682605599957334357820035222633779063185594791050580240543441090320215311599127137182
Poisson$(\lambda)$
5/2
bits:
2.641180198479715692042790979191877764391702715212450163151039267763513335847241238169855842712652037
Poisson$(\lambda)$
3
nats:
1.931470198148568933920429874127834053141403525336052813746881945019538729813054702547951673861818325
Poisson$(\lambda)$
3
bits:
2.786522476493763912625392660677598793417648784264444082499603201777175474140335917082785455885589506
Poisson$(\lambda)$
7/2
nats:
2.015172522512972281191703257567668482151311594224260979686239537574506009959929236249385425162933419
Poisson$(\lambda)$
7/2
bits:
2.907279404765168077763981946958716181565140299731930334643135942293590084967320392355186793891106727
Poisson$(\lambda)$
4
nats:
2.086672699880963843364905413809789785036141186912488866865116363393855498254560539498013526411849621
Poisson$(\lambda)$
4
bits:
3.010432356076650800573001069074024808015655368347941892641591307264329311555754173685781972285967802
Poisson$(\lambda)$
9/2
nats:
2.149057657291177720662766283583869089488940127886608659360632153135190596179776291374245081653255474
Poisson$(\lambda)$
9/2
bits:
3.100434824758435550997181059363749150563688468453148571200660433993762837860831402693911623626509882
Poisson$(\lambda)$
5
nats:
2.204395243428367907085868718265451070467333943465290792661037432762168690515573557212543455905145669
Poisson$(\lambda)$
5
bits:
3.180270085853325681614056203858280644121621748014434509458697795052746386504081507283025505277318451
Poisson$(\lambda)$
11/2
nats:
2.254128397205339932352588666478317114386028847864020174964231291683236504300151061310609361205464332
Poisson$(\lambda)$
11/2
bits:
3.252019860175131442525439909447227502047372674140368057392736866676977844171176147424120252998512405
Poisson$(\lambda)$
6
nats:
2.299299563162719628833883849800045225698348435423323454727939858103141962017085434319194087898010972
Poisson$(\lambda)$
6
bits:
3.317188077293015495639602812475706867310217218037655142815698360509239313845274138726121649581034856
Poisson$(\lambda)$
13/2
nats:
2.340684595915005417759062959845431555694587255351110902445735483368890061994314886984808320522044646
Poisson$(\lambda)$
13/2
bits:
3.376894058811765531713619702322029310999870731360610646323948074147436043736747185373883447486102309
Poisson$(\lambda)$
7
nats:
2.378875915025292790756490494142431101060468544485704306409238317403771896450309845448426578662224143
Poisson$(\lambda)$
7
bits:
3.431992485497185022879489609008425074874441390853514411247465825092867379581380835445612747992943408
Poisson$(\lambda)$
15/2
nats:
2.414335980371920956848660018534165662085899103747658224941220722760423680573272963984444957567045024
Poisson$(\lambda)$
15/2
bits:
3.483150545922364059340702927887187831910386129631038879933892121175569900975006475066036640978476130
Poisson$(\lambda)$
8
nats:
2.447432766544303521145548835547853824202579976376958155903602052273557668064215027567353141305212156
Poisson$(\lambda)$
8
bits:
3.530899115202622801642769555494344826907863480167108226115693723473248554820963499654229659457133342
Poisson$(\lambda)$
17/2
nats:
2.478463961751760384572910585812540462630704011338499817479853070593015375121234571232483361502084268
Poisson$(\lambda)$
17/2
bits:
3.575667666641278186549453571040999481535369738125960098441341029587031497697636499449120556096570763
Poisson$(\lambda)$
9
nats:
2.507673896080288983307899256236729597427714249478538371667415759186631878385724151976413858940196683
Poisson$(\lambda)$
9
bits:
3.617808694041738689192020417041845135204635804161951197483586803302070332816148388379208187632523594
Poisson$(\lambda)$
19/2
nats:
2.535265656177975599923122887122388088267447942333826643597252635247341844025305790685167167348694253
Poisson$(\lambda)$
19/2
bits:
3.657615189504069151528682240787388045777181971586049629857788124057767858975400124538181277122040463
Poisson$(\lambda)$
10
nats:
2.561409935274909122596534696011572878698544369530912100000667004818623769766638851673775509467973981
Poisson$(\lambda)$
10
bits:
3.695333411304832131328319876231498997315132843521031068595099901617290103726027857147682893950738059
Poisson$(\lambda)$
11
nats:
2.609914772529964161676277949405298375717912894829116304709278349102478813419169065582539960048254826
Poisson$(\lambda)$
11
bits:
3.765311099471826276535363975965011024604823913841807286257761630206720976366213409368797014795449274
Poisson$(\lambda)$
12
nats:
2.654119759193953918448335987878548541661362776799334656918587763835290057395884361905779329182442472
Poisson$(\lambda)$
12
bits:
3.829085414514527060808338882779417657276695424440188940110712685238850240503430676567908107201734572
Poisson$(\lambda)$
13
nats:
2.694726988440934805110961128293260498543857305929112398328495603968114266330653426695040349923164309
Poisson$(\lambda)$
13
bits:
3.887669262773387661846152043739604545190072991584634004461327060852813301161396284635288477828148974
Poisson$(\lambda)$
14
nats:
2.732279117514093289816313994292547256438650865354550028685514005388522950003731839614356520148584870
Poisson$(\lambda)$
14
bits:
3.941845533162055673478975141858786516297399989561695703619207833149758297773820733347130039947790525
Poisson$(\lambda)$
15
nats:
2.767204386781281645709122804666784127619841120604633162307118331245380942090578191697760008076242512
Poisson$(\lambda)$
15
bits:
3.992232045935540035642007804819096397176270482210215783708782093486466719098225811644873570063013614
Poisson$(\lambda)$
16
nats:
2.799846746366404883161529115997215534963651806403194667798276856182137929455106883845833280757558198
Poisson$(\lambda)$
16
bits:
4.039325016231911651304395676781591241896018381229093137751574699315737633201032297768672627042994624
Poisson$(\lambda)$
17
nats:
2.830486654592801591065821310765284142091578493426671526871562930910987791084869048303779491944531987
Poisson$(\lambda)$
17
bits:
4.083529059883427136088379824870694276952723411084483570969287226846491699267734110897036010382572312
Poisson$(\lambda)$
18
nats:
2.859355821508481381140110271800580190314589983190394980296541927767915649013136900939404306910534449
Poisson$(\lambda)$
18
bits:
4.125178463827274100445802854081470275331922590989326931749847361269307494498906843958151418188165731
Poisson$(\lambda)$
19
nats:
2.886647901001217788964592056359279022509628800407729944607314757041114728866668175279991185604526433
Poisson$(\lambda)$
19
bits:
4.164552611566992292021400797092547888372610023933355541736114425840975872630037189065582161043429559
Poisson$(\lambda)$
20
nats:
2.912526400182318058528039532827949715257857927145863882972145255583603459312485415107806276842359088
Poisson$(\lambda)$
20
bits:
4.201887394001214751472641352896721724969469810372668779240524121494806876950183971882121389614160943
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 2
nats:
0.7474814710871595424353002205959008132895071687690667637966026623611793342910689123605201166088516715
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 2
bits:
1.078387811493832155036127519996328468007821418919499578678169076587709370683088927073809404822971040
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 5
nats:
0.9950269901795212593824099014046464681916469702250978339087265011256030946130993020167734320217338660
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 5
bits:
1.435520504282666614090633760401527364261389152593528447547751755851121579695036449572261092414304176
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 8
nats:
0.7474814710871595424353002205959008132895071687690667637966026623611793342910689123605201166088516715
hypergeometric with population $N$, successes $K$, and draws $n$
10, 2, 8
bits:
1.078387811493832155036127519996328468007821418919499578678169076587709370683088927073809404822971040
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 2
nats:
0.9950269901795212593824099014046464681916469702250978339087265011256030946130993020167734320217338660
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 2
bits:
1.435520504282666614090633760401527364261389152593528447547751755851121579695036449572261092414304176
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 5
nats:
1.235866276237501437415733987203138056856872737446438208882059671380121793756824376566409242187707681
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 5
bits:
1.782978147929753081717861035505657921666942359953125499718248628755821319116336270569922458213986168
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 8
nats:
0.9950269901795212593824099014046464681916469702250978339087265011256030946130993020167734320217338660
hypergeometric with population $N$, successes $K$, and draws $n$
10, 5, 8
bits:
1.435520504282666614090633760401527364261389152593528447547751755851121579695036449572261092414304176
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 2
nats:
0.5172152102791041129553230505917346437690991633144458813666523863532445342889461111533164853628601624
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 2
bits:
0.7461838189420059150723366394158745644797403294939282785539353884294489532850532969532924198940674680
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 5
nats:
0.8496383026252035448134413853769020153464725539334277158947647840411483310544806008554235405745220360
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 5
bits:
1.225768965746697493617973394319184582304366813935560756306483475438373216736192802460358732329646111
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 10
nats:
1.020094373854497117875383236186510608448624328780448681460504608529814766433606037891406505153877138
hypergeometric with population $N$, successes $K$, and draws $n$
20, 2, 10
bits:
1.471685094398615244063493355225013427097456344992562161489360955080401215237848766597316160376424419
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 2
nats:
0.8496383026252035448134413853769020153464725539334277158947647840411483310544806008554235405745220360
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 2
bits:
1.225768965746697493617973394319184582304366813935560756306483475438373216736192802460358732329646111
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 5
nats:
1.247673279616172846414580108421158201190032728727577037910456851035242831454395745575001619265833728
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 5
bits:
1.800012053151921559224521579111895619063902103155378256424309736929313564440780981634547028902144749
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 10
nats:
1.410178992589031228652819447306708741437597768533311273935985517608637596611516046058897830503149884
hypergeometric with population $N$, successes $K$, and draws $n$
20, 5, 10
bits:
2.034458239373989634221859674560713137552345239847121861610699015808455486701181968646063973142589464
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 2
nats:
1.020094373854497117875383236186510608448624328780448681460504608529814766433606037891406505153877138
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 2
bits:
1.471685094398615244063493355225013427097456344992562161489360955080401215237848766597316160376424419
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 5
nats:
1.410178992589031228652819447306708741437597768533311273935985517608637596611516046058897830503149884
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 5
bits:
2.034458239373989634221859674560713137552345239847121861610699015808455486701181968646063973142589464
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 10
nats:
1.555951815188116695579963730964488847021215656874658798345139717291614830311643423806768088940376957
hypergeometric with population $N$, successes $K$, and draws $n$
20, 10, 10
bits:
2.244763967634076850971891622394606806258417704630886357073461114387040892888987441338589618719612136
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/2
nats:
0.8829244358028678611733744961944307354433879906766004350294190823427973390492067733167179077816810386
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/2
bits:
1.273790705012483395982892455866812915659499706530622071372273071913531835757766350845756697418032690
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/3
nats:
0.5957444426529752089282563657246481688718219798805927581642526774231175248251386656391035900374057623
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/3
bits:
0.8594775530526067848202872635752976425515522792528938072459351654796377067686578111829621668089720239
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/4
nats:
0.4616944452661272704618622200724521231693208414645724404058230192556863601350996894431734800131608207
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/4
bits:
0.6660842865914227603269938800400590287199881480149275216994252109417654285050799830833911066724897286
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/5
nats:
0.3815083617781486930406096444585622895676310367784354881304725093927229804815598207217323097148839578
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/5
bits:
0.5504002215950076730547759683670634669483144108551243294646871197679114329221134109077580761649880490
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/10
nats:
0.2146256733097977327700470387913745065872989396977681389797236452424608948005024455284672061437511875
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/10
bits:
0.3096393945314999423229881594359854230011559336076745152315600223435417085671692483856979602040546990
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/100
nats:
0.2321102775566973302810445104221910373527786712051397228330649448855862256222377561258880902086242395
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/100
bits:
0.3348643463704081003977642332066198415830972653492620874682251106165436145652340882829227768315821531
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
2/5
nats:
0.7061788655876288926642071811479487931411471438884746933673414058336740053652418585655866928108773796
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
2/5
bits:
1.018800747363866059365688926175843546945898479684331941292099793730973474069285541837774468063067580
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/10
nats:
0.5418157739122489522576475826452125732573836606703275355486977707221429474931634990483766019934520831
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/10
bits:
0.7816749300986173552056923867685365120957508368139526365608441035687344885581751659307654932882836696
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/20
nats:
0.1215266341136756774640045442685343357925434586528077911320573803791387894668658499703513042745031811
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/20
bits:
0.1753258723717274267926351251017078948954670421256346383536396957327758234461123596411401495288593893
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/20
nats:
0.2998607695400497698950501978394255172511096795852178088338520653467749202434928694341638823755478706
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/20
bits:
0.4326076451725781358046219991911120744333990471931319097580884737332961180973016476347827867314325003
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/20
nats:
0.6229757674728398294335345496568122110770601591313233008196115178482120717991974719202367211451530801
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/20
bits:
0.8987640503270620175935261335766212399859263942303274954936728760265860165539854371128569138960853759
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/20
nats:
0.7924483826286087192660174347592624254320690699017577723037162754465516829393168016586726418769405844
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/20
bits:
1.143261351778773575764225147757404249353306578089839728317617354113597897445392889525408320750290765
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/25
nats:
0.1011257352290939186657447970895655778158553412931118575870796673141407289029510080745294387913756845
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/25
bits:
0.1458935967212641383142663401204175182661646340422791098621239305303175441544994005299146984173598477
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
2/25
nats:
0.1787235278158125545353813102444569283272681380654577542276464685941744626936568587719432086190205369
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
2/25
bits:
0.2578435472700534822604551264881641995133663928847983665734440148556016975431534330553938092626756777
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/25
nats:
0.2493433856958248547222929917538728197049682088645256162017254175415838937683238461568505547189453378
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/25
bits:
0.3597264660218306123673930437157843504008719218367795724085641044419399625374825792479043813729349940
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
4/25
nats:
0.3163927268536472707174210219308378328049737994583297993976164887070407346959620761146057981931019163
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
4/25
bits:
0.4564582180050932799012767693686786764606310649058566185486802613180785039703707464425250168217043172
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
6/25
nats:
0.4457012002836763817335028338562996751261126032307218455860710412439941496478379257628822640045252579
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
6/25
bits:
0.6430109113675185665606563253559375184119281377039415369246541037706310789687954461529453250077039834
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/25
nats:
0.5097006350639865614087930771510274328676676410980788561479786585879169121145471260259945256556359685
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/25
bits:
0.7353425785447687080511201799061672232756448214613978380916591113986985675627752262566534243195811049
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
8/25
nats:
0.5740981152173436327702361598459248064915385549854346221532259795176598410630559880523820562728668030
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
8/25
bits:
0.8282485038077623976357215896989387926121104194916105315906874170697983563559316219888001331028557954
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/25
nats:
0.6394210962917866924908731157732275912945386406379546150806310722834253677344018786437540882080250425
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/25
bits:
0.9224896446599450104919530877780305729567551926163984112227307697187996870648435960175922530205878048
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/25
nats:
0.7748969228720023949905995484278266444463889815968045017525163288000907845675201118745559293174041456
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/25
bits:
1.117939947827555419030074816880121682783497636604018808344320546551029400175605701687339289061358159
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
12/25
nats:
0.8461483535679885584854497717271371536772886206242537288727729710475571427451355915984172493402107967
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
12/25
bits:
1.220734033548898319623497689166351716704676369172789850297874739628566232942323134168728144232489286
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/50
nats:
0.05687827217065897218392531987207706328031646218087692134065563404274293324892853791581382178306114360
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/50
bits:
0.08205800119494243533482120602456272630994937289817893283479342038136261968096920625326267237983933430
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/50
nats:
0.1411613854061891200260745154895495757125117918357074492618625579144722853482239387643148845278560611
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/50
bits:
0.2036528306905247349219157998039952460315893178426719743947771604455680601891112693477305289403395204
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/50
nats:
0.2831907801804933229308713623473248919560165507874007048124218595746496605787292690830221844286631424
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/50
bits:
0.4085579341918742626276531478490480281970748681249203035462390850252449063207177062794983961883174778
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/50
nats:
0.3491199813808595092020037489580434141871802588518366295378702149651526731065613466172919676577828006
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/50
bits:
0.5036736658134132530883274985016278869915339914050089980800495683933444801768975722497409746831525759
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/50
nats:
0.4136701298613424362600123820553279388842972251727344967740761440221813661714559199772233506599571656
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
11/50
bits:
0.5967998449148522286983975131915425393535326555152536283045263836953333937274452217176087299812486238
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
13/50
nats:
0.4776859584772374889076702395190766408831754033594705034842087561213145629426050493269336068275295635
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
13/50
bits:
0.6891551633974018154450674088212738961739550617129816821010312697258120711421291542062211808658150321
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
17/50
nats:
0.6066120953711656047428914335583988596842426343065297570144220171967791518388341168695884788393017453
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
17/50
bits:
0.8751562617352435322280649169250038633496663920857574528716712424960330908751168955531837506865024940
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
19/50
nats:
0.6725885357728190118043689277746100736228926021579570214867606350186780656581186451927812520483809277
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
19/50
bits:
0.9703401451182151516596922833420948119049277595095864660941659104702727738944328372937404143215795871
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
21/50
nats:
0.7402585292366616340448749501387742285789093968458811235548371598626269253688800434485064098349126090
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
21/50
bits:
1.067967309105489470072305378486611400822041628354155931881715171693773869217608857536181092566617205
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
23/50
nats:
0.8101673991510519056258150778706189459806554582101367719945939550171278054899425015899147709489644666
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
23/50
bits:
1.168824489045131966710158761157697729876751003127975373914936457293542038262793553294437549114854572
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/100
nats:
0.03172559864712491065204744782383799722065798791184414149819100294309049736514357106954282204907060155
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
1/100
bits:
0.04577036383744071513203359612058505732308547946993291156282767868578756824989740236606733703858875735
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/100
nats:
0.07971535118412993844169373052992024141586359443033099982169668073561117153682420137021505073366291480
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
3/100
bits:
0.1150049418360664191128740309883426061843167694451269933625645563704410741376942467866141583177137386
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/100
nats:
0.1601894779430489861608308736773549012020921593806028909128854513663282818769657533715953446518624676
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
7/100
bits:
0.2311045654310287589467196691871260827168378141271269895375332579349778446531256918533187638208325823
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/100
nats:
0.1968473208061305966332003570036245745329979849263478368843617876286488971830618833502577041980038756
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
9/100
bits:
0.2839906535392834783884489051925746343970014973491440655532557421090569282432011335900381980719972327
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
13/100
nats:
0.2663602463675179200884806937676403665789201425488423644557815106939551841207784804180780298022818873
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
13/100
bits:
0.3842766065243806326188651891151574946933476280296668146368059560561422889667254656429490857741897812
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
17/100
nats:
0.3328065429693575193247648007830542498335250036673032868640887271623401189965821100573342479779218155
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
17/100
bits:
0.4801383491172918035462595730499002526972298049285700372491208777571357598614377834636382093289949979
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
19/100
nats:
0.3653490616677734156324433031035959575063172122979517269959256945110331851407315832230302147251709783
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
19/100
bits:
0.5270872794615327813127195186085323177548800911067528285492373867170340203890774653655622064246578695
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
21/100
nats:
0.3976112597929846184577835413362759280119835843493317979582257314745961675644289749799325449718675004
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
21/100
bits:
0.5736317927049521961555805914460570459713415662956952535455634917343249093373480401467112665912350186
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
23/100
nats:
0.4296965029539503204408205024839233235962748954749048394665298031419354405486441924069379098086219003
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
23/100
bits:
0.6199210138989939431029699701850065660660693465803148960494820689385892689550772480352166469630503694
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
27/100
nats:
0.4936850390339537317330952820441637604398916479917606364624670194117657194931778699856117526455603508
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
27/100
bits:
0.7122369575753593748230680954840349797181108488158631574294459024408022994772175105026679497611179059
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
29/100
nats:
0.5257414053633178019925175436371555239826635736846395588619543075476162831504478005947826727545736626
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
29/100
bits:
0.7584845183076528619802775510162062422309501469973828132892071559479788780787712024343815932946783298
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
31/100
nats:
0.5579319785949505135369295931131409172026152634132130141328299616069250735222189941881185398935726253
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
31/100
bits:
0.8049256986723023876920129517402771872560329025427229130687603148897466010321169268647441703460884054
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
33/100
nats:
0.5903221777248257466461536571808776910741557630477783700887052778662747073528179015360567227823248422
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
33/100
bits:
0.8516548783303794041010946420185463896208158013686895297779323209930400357025604185052468346493329570
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
37/100
nats:
0.6559560185185333927951651295174023011584029414519068908824843072709509496208038732664915621983223444
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
37/100
bits:
0.9463444949579571711604417665547275231517204845868417583804417219114234957940863094512144657469063547
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
39/100
nats:
0.6893267444971231309445123010826161686908105342462054168165371289180836128990393514380441919331292942
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
39/100
bits:
0.9944882758381330868554052007930176091732237474959195359993923902851930272669911343055800430877503467
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
41/100
nats:
0.7231532740853972323549196518581580960307685923776401690115743321919365628635903644046999636694023922
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
41/100
bits:
1.043289642325619922122610345447551946595241511762883512839218453299255752550231967296416157406819940
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
43/100
nats:
0.7575034052242885789781145110031467698519779035073407296568576156539687156488638533293177879005843673
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
43/100
bits:
1.092846406173584028615303419379037624179444199997591291656635439289035168112826319372095618507388848
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
47/100
nats:
0.8280639378227940956229204559385638814317483333873801344032833238391980953083034576450890780258844826
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
47/100
bits:
1.194643736635931980375300902271579622430044028226807386302256547392158283955813173929026003489046272
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
49/100
nats:
0.8644314323527175624375302741190666494470979329329788907385670492553900799881937764468616512863430619
logarithmic series with parameter $p$ on $\{1,2,\ldots\}$
49/100
bits:
1.247110940643809069382807273872180532942625756135771122949497122115675415452383162591964642229955681
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
1, 10
nats:
1.993805759248670333856896957152200002515881919313234443059920928844971188262118361333737047027525301
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
1, 10
bits:
2.876453681363911178606028951957139062281746896843547256136816505700920738876608669920150793229488495
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
1, 100
nats:
3.680777745058364587712049705079120647154594445970691381230316568487131515270354840259475373983094601
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
1, 100
bits:
5.310239799410163827185483011220759943936550257290205835622511376440494925019213330118328210859206088
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
2, 10
nats:
1.236292605723536032606356156161327182303383428318270068948546189234125242762983312473959499140141832
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
2, 10
bits:
1.783593211365039932780342812340463340400287991633168443499177928725208975717239302939316395800895220
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
2, 100
nats:
1.570207647482339540162613521902729790654660931501783911692986346654237522483118263510973378003362037
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
2, 100
bits:
2.265330786188696882756995338066582442676759867526216877642268659046588803984839013505637568288465058
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
3, 10
nats:
0.6442558055995113636683707044605262008712346456536760077386418469395852710453585301768664047657016517
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
3, 10
bits:
0.9294646558023391069451494849023790272095154616243967468365773549318759638704603085592367034572303273
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
3, 100
nats:
0.6778500429477991599458253306331032238443757698120348972410214714176782424088989142075970344581527653
Zipfian with exponent $s$ on $\{1,\ldots,N\}$
3, 100
bits:
0.9779308954271607108279556980630223999262798214704322874823811143700003679754981901249003433872625061
Benford leading-digit distribution on $\{1,\ldots,9\}$
-
nats:
1.993433150791204269825208861305402097795519730691358225187074927657154761171872828137507030847518217
Benford leading-digit distribution on $\{1,\ldots,9\}$
-
bits:
2.875916120990131601775229975403237439422636996748531479535509615582896465138313864332778023188451518
